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(Data Sources: National Bureau of Statistics; The Economist)






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<article class="post-text h-entry hentry postpage" itemscope="itemscope" itemtype="http://schema.org/Article"><header><h1 class="p-name entry-title" itemprop="headline name"><a href="#" class="u-url">China-trillion-dollars-wasted-investment</a></h1>

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            <p class="byline author vcard"><span class="byline-name fn">
                    Tao Junjie
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            <p class="dateline"><a href="#" rel="bookmark"><time class="published dt-published" datetime="2015-06-24T13:43:59+08:00" itemprop="datePublished" title="2015-06-24 13:43">2015-06-24 13:43</time></a></p>
            
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<h2 id="Wasted-investment">Wasted investment<a class="anchor-link" href="china-trillion-dollars-wasted-investment.html#Wasted-investment">¶</a>
</h2>
<h4 id="China's-$6.8-trillion-hole?">China's <code>$6.8</code>-trillion hole?<a class="anchor-link" href="china-trillion-dollars-wasted-investment.html#China's-%246.8-trillion-hole?">¶</a>
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<p><em>(Data Sources: National Bureau of Statistics; The Economist)</em></p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">dficor</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_excel</span><span class="p">(</span><span class="s1">'china-1979-2013-icor.xlsx'</span><span class="p">,</span><span class="s1">'Sheet1'</span><span class="p">)</span>
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<p>HAS CHINA really blown <code>$6.8</code> trillion on <a href="http://wallstreetcn.com/node/211297">worthless investments</a> over the past five years? This is the startling claim made by two Chinese government researchers that has, understandably, <a href="http://www.reuters.com/article/2014/11/20/china-economy-investment-idUSL3N0TA2KP20141120">caused quite</a> <a href="http://www.ft.com/intl/cms/s/0/002a1978-7629-11e4-9761-00144feabdc0.html?siteedition=intl#axzz3KJdiuSo5">a stir</a>. If true, it would mean that fully 37% of Chinese investment since 2009 was wasted on building bridges to nowhere and homes with no one in them. There is, without question, plenty of worrying evidence that Chinese investment has become less efficient in recent years. But a closer look at how the researchers produced the <code>$6.8</code> trillion figure badly damages their claim. Calling it a back-of-the-envelope estimate would be undeserved praise.</p>

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<p>The <code>$6.8</code> trillion calculation was made by Xu Ce of the National Development and Reform Commission, an economic planning agency, and Wang Yuan of the Academy of Macroeconomic Research, a think-tank under the commission. Their analysis was published last week as an <a href="http://money.163.com/14/1120/02/ABF8SCQQ00253B0H.html">opinion piece</a> in the Shanghai Securities Journal, a government-run newspaper. In their article, they estimate that worthless investment totalled 7.9 trillion yuan in 2009; 5.4 trillion yuan in 2010; 4.7 trillion yuan in 2011; 10.6 trillion yuan in 2012; and 13.2 trillion yuan last year. That amounts to 41.8 trillion yuan over the past five years, or <code>$6.8</code> trillion at the current exchange rate.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">dficor</span>
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<div style="max-height:1000px;max-width:1500px;overflow:auto;">
<table border="1" class="dataframe">
<thead><tr style="text-align: right;">
<th></th>
      <th>Investment(￥)</th>
      <th>Added GDP(￥)</th>
      <th>ICOR</th>
    </tr></thead>
<tbody>
<tr>
<th>2013</th>
      <td> 28036</td>
      <td> 5727</td>
      <td> 4.90</td>
    </tr>
<tr>
<th>2012</th>
      <td> 25277</td>
      <td> 5678</td>
      <td> 4.45</td>
    </tr>
<tr>
<th>2011</th>
      <td> 22834</td>
      <td> 6980</td>
      <td> 3.27</td>
    </tr>
<tr>
<th>2010</th>
      <td> 19360</td>
      <td> 5404</td>
      <td> 3.58</td>
    </tr>
<tr>
<th>2009</th>
      <td> 16446</td>
      <td> 3280</td>
      <td> 5.01</td>
    </tr>
<tr>
<th>2008</th>
      <td> 13833</td>
      <td> 4938</td>
      <td> 2.80</td>
    </tr>
<tr>
<th>2007</th>
      <td> 11094</td>
      <td> 4389</td>
      <td> 2.53</td>
    </tr>
<tr>
<th>2006</th>
      <td>  9295</td>
      <td> 3529</td>
      <td> 2.63</td>
    </tr>
<tr>
<th>2005</th>
      <td>  7786</td>
      <td> 2647</td>
      <td> 2.94</td>
    </tr>
<tr>
<th>2004</th>
      <td>  6917</td>
      <td> 2434</td>
      <td> 2.84</td>
    </tr>
<tr>
<th>2003</th>
      <td>  5596</td>
      <td> 1614</td>
      <td> 3.47</td>
    </tr>
<tr>
<th>2002</th>
      <td>  4557</td>
      <td> 1145</td>
      <td> 3.98</td>
    </tr>
<tr>
<th>2001</th>
      <td>  3977</td>
      <td> 1028</td>
      <td> 3.87</td>
    </tr>
<tr>
<th>2000</th>
      <td>  3484</td>
      <td>  762</td>
      <td> 4.57</td>
    </tr>
<tr>
<th>1999</th>
      <td>  3295</td>
      <td>  459</td>
      <td> 7.17</td>
    </tr>
<tr>
<th>1998</th>
      <td>  3131</td>
      <td>  487</td>
      <td> 6.43</td>
    </tr>
<tr>
<th>1997</th>
      <td>  2997</td>
      <td>  749</td>
      <td> 4.00</td>
    </tr>
<tr>
<th>1996</th>
      <td>  2878</td>
      <td> 1095</td>
      <td> 2.63</td>
    </tr>
<tr>
<th>1995</th>
      <td>  2547</td>
      <td> 1300</td>
      <td> 1.96</td>
    </tr>
<tr>
<th>1994</th>
      <td>  2034</td>
      <td> 1328</td>
      <td> 1.53</td>
    </tr>
<tr>
<th>1993</th>
      <td>  1572</td>
      <td>  937</td>
      <td> 1.68</td>
    </tr>
<tr>
<th>1992</th>
      <td>  1009</td>
      <td>  499</td>
      <td> 2.02</td>
    </tr>
<tr>
<th>1991</th>
      <td>   787</td>
      <td>  323</td>
      <td> 2.44</td>
    </tr>
<tr>
<th>1990</th>
      <td>   675</td>
      <td>  204</td>
      <td> 3.31</td>
    </tr>
<tr>
<th>1989</th>
      <td>   633</td>
      <td>  192</td>
      <td> 3.29</td>
    </tr>
<tr>
<th>1988</th>
      <td>   570</td>
      <td>  311</td>
      <td> 1.83</td>
    </tr>
<tr>
<th>1987</th>
      <td>   446</td>
      <td>  177</td>
      <td> 2.52</td>
    </tr>
<tr>
<th>1986</th>
      <td>   394</td>
      <td>  143</td>
      <td> 2.75</td>
    </tr>
<tr>
<th>1985</th>
      <td>   346</td>
      <td>  171</td>
      <td> 2.02</td>
    </tr>
<tr>
<th>1984</th>
      <td>   252</td>
      <td>  115</td>
      <td> 2.19</td>
    </tr>
<tr>
<th>1983</th>
      <td>   204</td>
      <td>   63</td>
      <td> 3.26</td>
    </tr>
<tr>
<th>1982</th>
      <td>   178</td>
      <td>   58</td>
      <td> 3.07</td>
    </tr>
<tr>
<th>1981</th>
      <td>   163</td>
      <td>   42</td>
      <td> 3.92</td>
    </tr>
<tr>
<th>1980</th>
      <td>   160</td>
      <td>   50</td>
      <td> 3.20</td>
    </tr>
<tr>
<th>1979</th>
      <td>   148</td>
      <td>   49</td>
      <td> 3.04</td>
    </tr>
</tbody>
</table>
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<p>These are remarkably precise figures for wasted investment, something that, by its nature, is extremely hard to pin down. There are practical difficulties – for example, we know that some government investment funds have been skimmed off by corrupt officials, but it takes careful forensics to track the ill-gotten gains of one rotten official, let alone thousands of them. Even greater are the theoretical challenges. China has clearly built too many homes, too quickly, but if some of those that stand empty today are eventually bought then what once seemed a wasted investment could yet turn into a productive one.</p>

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<p>So how exactly do Mr Xu and Ms Wang arrive at their numbers? Their method is to compare China’s capital efficiency in the 1980s and 1990s with the past decade; they treat any decline in efficiency as evidence of wasted investment. Although they don’t publish their calculations in full, their conclusions have the virtue of being very easy to replicate from official data. (Be warned that this is slightly wonky.)</p>

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<p>Mr Xu and Ms Wang base their analysis entirely on the concept of <a href="http://www.investopedia.com/terms/i/icor.asp">incremental capital output ratio, or ICOR</a>. ICOR is a measure of how much investment it takes to produce each additional unit of growth in an economy, with investment the numerator and additional GDP the denominator. The higher a country’s ICOR, the less efficient it is – that is, it takes more investment to produce a smaller amount of economic output.</p>

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$$ICOR = \frac {Annual\ Investment} {Annual\ Added\ GDP} $$
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 计算指定时间段begin,end的ICOR均值</span>
<span class="k">def</span> <span class="nf">icor_average</span><span class="p">(</span><span class="n">begin</span><span class="p">,</span><span class="n">end</span><span class="p">):</span>
    <span class="n">icor</span> <span class="o">=</span> <span class="n">dficor</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">end</span><span class="p">:</span><span class="n">begin</span><span class="p">]</span>
    <span class="n">icor</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="s1">'</span><span class="si">{1}</span><span class="s1">_</span><span class="si">{0}</span><span class="s1">_Average'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">begin</span><span class="p">,</span><span class="n">end</span><span class="p">),</span><span class="s1">'ICOR'</span><span class="p">]</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">icor</span><span class="o">.</span><span class="n">loc</span><span class="p">[:,</span><span class="s1">'ICOR'</span><span class="p">]</span><span class="o">.</span><span class="n">mean</span><span class="p">(),</span><span class="mi">2</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">icor</span>
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<p>Mr Xu and Ms Wang begin by calculating that China’s average ICOR from 1979 to 1996 was 2.6. To do so they tot up each year’s ICOR and calculate a simple average. Here is a table of all of China's ICORs from 1979 to 1996, yielding the same average that they calculate:</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">icor_average</span><span class="p">(</span><span class="mi">1979</span><span class="p">,</span><span class="mi">1996</span><span class="p">)</span>
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<div style="max-height:1000px;max-width:1500px;overflow:auto;">
<table border="1" class="dataframe">
<thead><tr style="text-align: right;">
<th></th>
      <th>Investment(￥)</th>
      <th>Added GDP(￥)</th>
      <th>ICOR</th>
    </tr></thead>
<tbody>
<tr>
<th>1996</th>
      <td> 2878</td>
      <td> 1095</td>
      <td> 2.63</td>
    </tr>
<tr>
<th>1995</th>
      <td> 2547</td>
      <td> 1300</td>
      <td> 1.96</td>
    </tr>
<tr>
<th>1994</th>
      <td> 2034</td>
      <td> 1328</td>
      <td> 1.53</td>
    </tr>
<tr>
<th>1993</th>
      <td> 1572</td>
      <td>  937</td>
      <td> 1.68</td>
    </tr>
<tr>
<th>1992</th>
      <td> 1009</td>
      <td>  499</td>
      <td> 2.02</td>
    </tr>
<tr>
<th>1991</th>
      <td>  787</td>
      <td>  323</td>
      <td> 2.44</td>
    </tr>
<tr>
<th>1990</th>
      <td>  675</td>
      <td>  204</td>
      <td> 3.31</td>
    </tr>
<tr>
<th>1989</th>
      <td>  633</td>
      <td>  192</td>
      <td> 3.29</td>
    </tr>
<tr>
<th>1988</th>
      <td>  570</td>
      <td>  311</td>
      <td> 1.83</td>
    </tr>
<tr>
<th>1987</th>
      <td>  446</td>
      <td>  177</td>
      <td> 2.52</td>
    </tr>
<tr>
<th>1986</th>
      <td>  394</td>
      <td>  143</td>
      <td> 2.75</td>
    </tr>
<tr>
<th>1985</th>
      <td>  346</td>
      <td>  171</td>
      <td> 2.02</td>
    </tr>
<tr>
<th>1984</th>
      <td>  252</td>
      <td>  115</td>
      <td> 2.19</td>
    </tr>
<tr>
<th>1983</th>
      <td>  204</td>
      <td>   63</td>
      <td> 3.26</td>
    </tr>
<tr>
<th>1982</th>
      <td>  178</td>
      <td>   58</td>
      <td> 3.07</td>
    </tr>
<tr>
<th>1981</th>
      <td>  163</td>
      <td>   42</td>
      <td> 3.92</td>
    </tr>
<tr>
<th>1980</th>
      <td>  160</td>
      <td>   50</td>
      <td> 3.20</td>
    </tr>
<tr>
<th>1979</th>
      <td>  148</td>
      <td>   49</td>
      <td> 3.04</td>
    </tr>
<tr>
<th>1996_1979_Average</th>
      <td>  NaN</td>
      <td>  NaN</td>
      <td> 2.59</td>
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<p>For the next step, they calculate the ICORs from 1997 to 2013. Here is the table for that. As in Mr Xu and Ms Wang’s article, the average ICOR is 4.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">icor_average</span><span class="p">(</span><span class="mi">1997</span><span class="p">,</span><span class="mi">2013</span><span class="p">)</span>
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<table border="1" class="dataframe">
<thead><tr style="text-align: right;">
<th></th>
      <th>Investment(￥)</th>
      <th>Added GDP(￥)</th>
      <th>ICOR</th>
    </tr></thead>
<tbody>
<tr>
<th>2013</th>
      <td> 28036</td>
      <td> 5727</td>
      <td> 4.90</td>
    </tr>
<tr>
<th>2012</th>
      <td> 25277</td>
      <td> 5678</td>
      <td> 4.45</td>
    </tr>
<tr>
<th>2011</th>
      <td> 22834</td>
      <td> 6980</td>
      <td> 3.27</td>
    </tr>
<tr>
<th>2010</th>
      <td> 19360</td>
      <td> 5404</td>
      <td> 3.58</td>
    </tr>
<tr>
<th>2009</th>
      <td> 16446</td>
      <td> 3280</td>
      <td> 5.01</td>
    </tr>
<tr>
<th>2008</th>
      <td> 13833</td>
      <td> 4938</td>
      <td> 2.80</td>
    </tr>
<tr>
<th>2007</th>
      <td> 11094</td>
      <td> 4389</td>
      <td> 2.53</td>
    </tr>
<tr>
<th>2006</th>
      <td>  9295</td>
      <td> 3529</td>
      <td> 2.63</td>
    </tr>
<tr>
<th>2005</th>
      <td>  7786</td>
      <td> 2647</td>
      <td> 2.94</td>
    </tr>
<tr>
<th>2004</th>
      <td>  6917</td>
      <td> 2434</td>
      <td> 2.84</td>
    </tr>
<tr>
<th>2003</th>
      <td>  5596</td>
      <td> 1614</td>
      <td> 3.47</td>
    </tr>
<tr>
<th>2002</th>
      <td>  4557</td>
      <td> 1145</td>
      <td> 3.98</td>
    </tr>
<tr>
<th>2001</th>
      <td>  3977</td>
      <td> 1028</td>
      <td> 3.87</td>
    </tr>
<tr>
<th>2000</th>
      <td>  3484</td>
      <td>  762</td>
      <td> 4.57</td>
    </tr>
<tr>
<th>1999</th>
      <td>  3295</td>
      <td>  459</td>
      <td> 7.17</td>
    </tr>
<tr>
<th>1998</th>
      <td>  3131</td>
      <td>  487</td>
      <td> 6.43</td>
    </tr>
<tr>
<th>1997</th>
      <td>  2997</td>
      <td>  749</td>
      <td> 4.00</td>
    </tr>
<tr>
<th>2013_1997_Average</th>
      <td>   NaN</td>
      <td>  NaN</td>
      <td> 4.03</td>
    </tr>
</tbody>
</table>
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<p>These numbers are fine for what they are – estimates of the efficiency of Chinese investment – but it is at this point that the two researchers make several unreasonable leaps of logic. First, they use the 1979-96 ICOR average of 2.6 as their baseline estimate of what China’s ICOR ought to be were its investments all efficient. Next, they calculate the difference in China’s investment efficiency from 2009-13. For example, in 2009, the ICOR was 5, which is 48% less efficient than the baseline ICOR of 2.6. Therefore, they conclude, 48% of all Chinese investment in 2009 – 7.9 trillion yuan – was worthless. Similar calculations for each year up until 2013 yields the eye-popping result that 41.8 trillion yuan has been wasted.</p>

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$$ Efficiency\ of\ Investment = \frac {1979-96\ ICOR\ average\ as\ baseline\ ICOR} {China’s\ investment\ efficiency\ from\ 2009-13}*100\% $$$$ Worthless\ Investment = Investment*(1 - Efficiency\ of\ Investment) $$
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">worthlessInvt</span><span class="p">(</span><span class="n">begin</span><span class="p">,</span><span class="n">end</span><span class="p">,</span><span class="n">baselineICOR</span><span class="p">):</span>
    <span class="n">WorthlessInvt</span> <span class="o">=</span> <span class="n">dficor</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">end</span><span class="p">:</span><span class="n">begin</span><span class="p">]</span>
    <span class="n">WorthlessInvt</span><span class="p">[</span><span class="s1">'WorthlessInvt pct'</span><span class="p">]</span> <span class="o">=</span> <span class="n">WorthlessInvt</span><span class="o">.</span><span class="n">loc</span><span class="p">[:,</span><span class="s1">'ICOR'</span><span class="p">]</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="mi">1</span><span class="o">-</span><span class="n">baselineICOR</span><span class="o">/</span><span class="n">x</span><span class="p">)</span>
    <span class="n">WorthlessInvt</span><span class="p">[</span><span class="s1">'WorthlessInvt'</span><span class="p">]</span> <span class="o">=</span> <span class="n">WorthlessInvt</span><span class="o">.</span><span class="n">loc</span><span class="p">[:,</span><span class="sa">u</span><span class="s1">'Investment(￥)'</span><span class="p">]</span> <span class="o">*</span> <span class="n">WorthlessInvt</span><span class="o">.</span><span class="n">loc</span><span class="p">[:,</span><span class="s1">'WorthlessInvt pct'</span><span class="p">]</span>
    <span class="n">WorthlessInvt</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="s1">'</span><span class="si">{1}</span><span class="s1">_</span><span class="si">{0}</span><span class="s1">_Total'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">begin</span><span class="p">,</span><span class="n">end</span><span class="p">),</span><span class="s1">'WorthlessInvt'</span><span class="p">]</span> <span class="o">=</span> <span class="n">WorthlessInvt</span><span class="o">.</span><span class="n">loc</span><span class="p">[:,</span><span class="s1">'WorthlessInvt'</span><span class="p">]</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
    <span class="k">return</span> <span class="n">WorthlessInvt</span>
</pre></div>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">worthlessInvt</span><span class="p">(</span><span class="mi">2009</span><span class="p">,</span> <span class="mi">2013</span><span class="p">,</span> <span class="mf">2.59</span><span class="p">)</span>
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<thead><tr style="text-align: right;">
<th></th>
      <th>Investment(￥)</th>
      <th>Added GDP(￥)</th>
      <th>ICOR</th>
      <th>WorthlessInvt pct</th>
      <th>WorthlessInvt</th>
    </tr></thead>
<tbody>
<tr>
<th>2013</th>
      <td> 28036</td>
      <td> 5727</td>
      <td> 4.90</td>
      <td> 0.471429</td>
      <td> 13216.971429</td>
    </tr>
<tr>
<th>2012</th>
      <td> 25277</td>
      <td> 5678</td>
      <td> 4.45</td>
      <td> 0.417978</td>
      <td> 10565.217978</td>
    </tr>
<tr>
<th>2011</th>
      <td> 22834</td>
      <td> 6980</td>
      <td> 3.27</td>
      <td> 0.207951</td>
      <td>  4748.354740</td>
    </tr>
<tr>
<th>2010</th>
      <td> 19360</td>
      <td> 5404</td>
      <td> 3.58</td>
      <td> 0.276536</td>
      <td>  5353.743017</td>
    </tr>
<tr>
<th>2009</th>
      <td> 16446</td>
      <td> 3280</td>
      <td> 5.01</td>
      <td> 0.483034</td>
      <td>  7943.976048</td>
    </tr>
<tr>
<th>2013_2009_Total</th>
      <td>   NaN</td>
      <td>  NaN</td>
      <td>  NaN</td>
      <td>      NaN</td>
      <td> 41828.263211</td>
    </tr>
</tbody>
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<p>There are two major, indeed fatal, flaws in this. First, why have they chosen 1979-96 as their baseline for ICOR efficiency in China? A quick glance at the tables above reveals that there was a big jump in ICOR (that is, a big decline in efficiency) from 1997-2000, followed by an improvement. The 1979-96 selection leads to a sharp downward bias in their baseline estimate. If we break the ICOR into decades, and break out the past five years separately, the results are very different, as this table shows.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">new_icor</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">concat</span><span class="p">(</span><span class="n">icor_average</span><span class="p">(</span><span class="o">*</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">tail</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[(</span><span class="mi">1980</span><span class="p">,</span><span class="mi">1989</span><span class="p">),(</span><span class="mi">1990</span><span class="p">,</span><span class="mi">1999</span><span class="p">),(</span><span class="mi">2000</span><span class="p">,</span><span class="mi">2008</span><span class="p">),(</span><span class="mi">2009</span><span class="p">,</span><span class="mi">2013</span><span class="p">)])</span>
<span class="n">new_icor</span>
</pre></div>

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<table border="1" class="dataframe">
<thead><tr style="text-align: right;">
<th></th>
      <th>Investment(￥)</th>
      <th>Added GDP(￥)</th>
      <th>ICOR</th>
    </tr></thead>
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<tr>
<th>1989_1980_Average</th>
      <td>NaN</td>
      <td>NaN</td>
      <td> 2.81</td>
    </tr>
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<th>1999_1990_Average</th>
      <td>NaN</td>
      <td>NaN</td>
      <td> 3.32</td>
    </tr>
<tr>
<th>2008_2000_Average</th>
      <td>NaN</td>
      <td>NaN</td>
      <td> 3.29</td>
    </tr>
<tr>
<th>2013_2009_Average</th>
      <td>NaN</td>
      <td>NaN</td>
      <td> 4.24</td>
    </tr>
</tbody>
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<p>Using Mr Xu and Ms Wang’s method for calculating efficiency differences, we now can compare the ICOR of 4.2 over the past five years with 3.3, the average for both of the previous two decades. This is a much more relevant yardstick than the pre-1997 era. On this revised basis, China’s investments after the global financial were 21% less efficient than in the 1990-2008 period. Sticking to Mr Xu and Ms Wang’s approach, this would mean that 21% of all investment over the past five years – 22.6 trillion yuan (<code>$3.7</code> trillion) – had been wasted. That is still a lot of money to burn through, but it is almost half their headline-grabbing estimate.</p>

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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">worthlessInvt</span><span class="p">(</span><span class="mi">2009</span><span class="p">,</span> <span class="mi">2013</span><span class="p">,</span> <span class="mf">3.3</span><span class="p">)</span>
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<th></th>
      <th>Investment(￥)</th>
      <th>Added GDP(￥)</th>
      <th>ICOR</th>
      <th>WorthlessInvt pct</th>
      <th>WorthlessInvt</th>
    </tr></thead>
<tbody>
<tr>
<th>2013</th>
      <td> 28036</td>
      <td> 5727</td>
      <td> 4.90</td>
      <td> 0.326531</td>
      <td>  9154.612245</td>
    </tr>
<tr>
<th>2012</th>
      <td> 25277</td>
      <td> 5678</td>
      <td> 4.45</td>
      <td> 0.258427</td>
      <td>  6532.258427</td>
    </tr>
<tr>
<th>2011</th>
      <td> 22834</td>
      <td> 6980</td>
      <td> 3.27</td>
      <td>-0.009174</td>
      <td>  -209.486239</td>
    </tr>
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<th>2010</th>
      <td> 19360</td>
      <td> 5404</td>
      <td> 3.58</td>
      <td> 0.078212</td>
      <td>  1514.189944</td>
    </tr>
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<th>2009</th>
      <td> 16446</td>
      <td> 3280</td>
      <td> 5.01</td>
      <td> 0.341317</td>
      <td>  5613.305389</td>
    </tr>
<tr>
<th>2013_2009_Total</th>
      <td>   NaN</td>
      <td>  NaN</td>
      <td>  NaN</td>
      <td>      NaN</td>
      <td> 22604.879767</td>
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<p>That leads to the second and even bigger flaw – namely, this is a lousy method for calculating wasted investment. ICOR serves as a rough guide to the efficiency of investment. It does not, however, show how much money was been wasted, only that it is generating smaller or bigger growth returns compared with previous years. For example, say that an investment of <code>$1000</code> boosts GDP by <code>$500</code> this year, but only by <code>$400</code> next year. In this case, ICOR will have risen from 2 to 2.5. Using Mr Xu and Ms Wang’s framework, because investment is 20% less efficient in the second year than it was in the first year (ICOR of 2.5 vs 2), this is tantamount to 20% of investment, or <code>$200</code>, being worthless. But that is completely absurd. All we can conclude is that the return on investment has fallen, not that <code>$200</code> has been wasted. Moreover, it is inevitable that in years when investment soars – which was, after all, the point of China’s stimulus package – investment returns will appear to suffer. The real question is whether those investments deliver returns over time, hence the point in looking at average ICORs over a longer period.</p>

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<p>None of this is to give the Chinese economy a clean bill of health. As we have written, <a href="http://www.economist.com/news/leaders/21625785-its-debt-will-not-drag-down-world-economy-it-risks-zombifying-countrys-financial">debt</a> has increased too quickly, and declines in both productivity and investment efficiency are <a href="http://www.economist.com/news/finance-and-economics/21623708-weakening-productivity-casting-doubt-sustainability-chinas">worrisome</a>. But <code>$6.8</code> trillion down the drain in just five years? This at least is one thing that will not keep us up at night.</p>

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